Question

Consider a project to produce solar water heaters. It requires a $10 million investment and offers a level after-tax cash flow of $1.56 million per year for 10 years. The opportunity cost of capital is 9.25%, which reflects the project’s business risk.

a. Suppose the project is financed with $4 million of debt and $6 million of equity. The interest rate is 5.25% and the marginal tax rate is 21%. An equal amount of the debt will be repaid in each year of the project's life. Calculate APV. (Enter your answer in dollars, not millions of dollars. Do not round intermediate calculations. Round your answer to the nearest whole number.)

b. If the firm incurs issue costs of $730,000 to raise the $6 million of required equity, what will be the APV? (Enter your answer in dollars, not millions of dollars. Do not round intermediate calculations. Round your answer to the nearest whole number. Negative amount shoud be indicated by a minus sign.)

Answer 1

a)

The Adjusted present value (APV) = NPV + PV of debt tax shield

Year	Amount of debt	Interest tax shield	PV Factor	PV of interest tax shield
1	4,000,000	44100	0.950118765	41900.23753
2	3600000	39690	0.902725667	35829.18174
3	3200000	35280	0.857696596	30259.53591
4	2800000	30870	0.81491363	25156.38377
5	2400000	26460	0.774264732	20487.04481
6	2000000	22050	0.735643451	16220.93809
7	1600000	17640	0.698948647	12329.45413
8	1200000	13230	0.664084225	8785.834297
9	800000	8820	0.630958884	5565.057354
10	400000	4410	0.599485875	2643.73271
Total PV of tax-shield	199177.4003

Year	Cash-flows	PV Factor	PV of cash-flows
0	-10,000,000	1	-10000000
1	1560000	0.915331808	1427917.62
2	1560000	0.837832318	1307018.417
3	1560000	0.766894571	1196355.53
4	1560000	0.701962994	1095062.27
5	1560000	0.642529056	1002345.327
6	1560000	0.588127282	917478.5605
7	1560000	0.538331609	839797.3094
8	1560000	0.492752044	768693.1893
9	1560000	0.45103162	703609.3266
10	1560000	0.412843588	644035.9969
Net present value	-97686.4531

The Adjusted present value (APV) = NPV + PV of debt tax shield

APV = -97686.45 + 199177.40

APV = $101491

(b)

The costs of $730,000 to raise the $6 million of required equity are the floatation costs

APV (with floatation costs) = NPV + PV of debt tax shield - flotation cost

Hence, APV = -97686.45 + 199177.40 - 730000 = - 628509.05

APV = -$628509